Developing a general research framework for long COVID using causal modelling

Abstract

Background

Long COVID is an infection-associated chronic condition with uncertain evolution, leading to ambiguity in case definitions and various hypotheses about its pathophysiology. Despite this diversity, causal models may offer a unified understanding of post-acute COVID-19 mechanisms. This study aimed to examine whether dynamic Bayesian networks could facilitate inferences on long COVID.

Methods

Using a causal engineering approach, we developed directed acyclic graphs and qualitatively parametrised them as Bayesian networks to depict the hypothesised mechanisms of long COVID in a theory-agnostic manner. Based on the literature and expert knowledge, we created a general modelling framework summarising biological pathways from mild or severe COVID-19 to the development of respiratory symptoms and fatigue over four key periods (t₁ to t₄). We used qualitative parametrisation for design and validation, and tested the framework against four scenarios: A) mild COVID-19 at t₁ (start of acute infection); B) severe acute COVID-19 at t₁; C) symptoms reported at t₁ (acute COVID-19 disease); and D) symptoms reported at t₁ and t₃ (e.g., 3-to-6 months post-acute infection), indicating long COVID.

Results

Here we show that, in scenario A, the probability of progressing to severe disease and developing persistent organ dysfunction 1-to-2 years post-acute COVID-19 was lower than in scenario C. Those reporting symptoms at t₁ and t₃ have the highest probability of developing persistent organ dysfunction beyond the acute infection period.

Conclusions

Our findings lay the foundations for a better understanding of the progression of long COVID syndromes. Illustrative simulations support the use of causal models to help address both diagnostic and prognostic questions in long COVID research.

Plain Language Summary

Long COVID can affect some people after having COVID-19. It usually starts within three months of infection and can last for at least two months. People with long COVID may struggle with work, daily tasks, and social activities. Researchers find it hard to study because its causes aren’t directly visible. This study uses diagrams to show expert ideas about what might cause long COVID and how symptoms relate to those causes. By looking at four examples, it shows how explanations can change when new information appears. The approach helps researchers think in terms of “cause and effect”, which can improve understanding and communication about long COVID. It could also guide clinical trials, public health studies, and experiments.

Pérez Chacón et al. develop a causal modelling framework to guide diagnosis and prognosis of long COVID. The framework based on modelling scenarios involving expert knowledge, qualitative parameters, and statistical simulations can predict progression to severe and persistent organ dysfunction associated with long COVID beyond the acute infection.

INTRODUCTION

Between 2020 and 2021, a global estimate of the prevalence of self-reported fatigue, respiratory symptoms, and cognitive decline spanning at least 3 months from the onset of SARS-CoV-2 infection has been put at 6.2% (95% uncertainty interval, 2.4–13.3%)¹. The low precision of this interval reflects heterogeneous and limited data which hamper our understanding of the series of complex conditions that can arise after the acute phase of COVID-19. These conditions are generally referred to in the literature as post-acute sequelae of COVID-19, or ‘long COVID’.

The hypothesised pathobiological drivers of long COVID have included the presence of SARS- CoV-2 reservoirs, tissue damage and dysfunction triggered by inflammation, immune dysregulation, mitochondrial dysfunction, and reactivation of Epstein-Barr virus (EBV) or other latent viruses^2–6. However, in order to answer (quantitative) causal questions, we need to understand the causal pathways that link long COVID symptoms to their proposed underpinning mechanisms³. This effort has been stymied by the lack of a common language and the diversity of long COVID definitions (Supplementary Information [Supplementary Table 1]).

To overcome these obstacles, we propose a causal modelling approach that harmonises operational case definitions and pathological mechanisms of long COVID using causal directed acyclic graphs (DAGs) and Bayesian networks (BNs). A DAG is a graphical model that depicts assumptions about the relationship between nodes (variables) using arcs (arrows) which go from one node to the other, with no directed cycles. A BN is a DAG in which the dependencies between the nodes are represented by a series of conditional probability distributions (Fig. 1)⁷. In a causal DAG or BN, arcs depict direct causal influences, with the direction of the arc representing possible processes that can lead to changes in the child node.

Fig. 1. Simple two-node example of a Bayesian network describing the probabilistic relationship between disease and symptoms with variation in the availability of evidence.

Here we show probabilities for all nodes when there is: (a) no evidence; evidence of (b) mild disease or (c) no mild disease; evidence of (d) reported symptoms or (e) symptoms not reported. The marginal probability distribution for each node is represented as a bar chart, showing the marginal probabilities for each state. Colours are used solely to distinguish states in a distribution.

Therefore, a causal BN allows quantitative causal reasoning in an uncertain domain, based on a graphical structure (a DAG) coupled with associated conditional probability estimates⁷. The nodes in a BN depict a set of random variables from the domain. The arcs represent direct (unmediated) dependencies which are causal when used to encode causal knowledge⁷. Assuming discrete variables, the direct causal dependencies are quantified by conditional probability distributions or tables associated with each node.

For example, Fig. 1 shows a simple BN with two nodes: ‘Mild Disease’ (M) and ‘Symptoms’ (S). In this example, M has an unconditional discrete probability distribution:

$$P\left(M\right)=⟨\mathrm{Yes}=0.1,\mathrm{No}=0.9⟩$$ 1

Since mild disease causally influences the reporting of symptoms, S is made conditional on M to represent the direction of that influence, with the conditional probability distribution:

$$P\left(S\mid M\right)=\left\{\begin{array}{cc}⟨\mathrm{Reported}=0.606,\mathrm{Not\; reported}=0.394⟩\hfill & \mathrm{if}M=\mathrm{Yes}\hfill \\ ⟨\mathrm{Reported}=0.019,\mathrm{Not\; reported}=0.981⟩\hfill & \mathrm{if}M=\mathrm{No}\hfill \end{array}\right)$$ 2

Encoding causal knowledge in a DAG allows one to identify potential issues with statistical inference ahead of an analysis (such as contextual and definitional differences, as well as the impact from confounding, selection bias, and measurement error on causal effect estimates) and points to opportunities for resolving them⁸. Furnishing the DAG with probabilities based on prior knowledge yields a BN and, in so doing, a stronger test of the causal knowledge. The predictions of a BN can be updated along the patient’s clinical course, utilising as little or as much information as may become available over time⁷, lending their use to decision support in settings where information may be evolving and/or sparse. BNs can be used to model systems that change over time (e.g., dynamic systems) using sequential data. These dynamic BNs are state-space models that explicitly represent the role of time in the problem domain of interest⁹.

In addition to SARS-CoV-2, historically, various pathogens have been associated with the development of post-infectious disability in a small subset of patients. The clinical manifestations of these post-infectious syndromes pose substantial diagnostic difficulties, and the underlying mechanisms are not well understood¹⁰. Using long COVID as a case study, here we demonstrate how a causal modelling approach (in the form of causal DAGs and BNs) can help depict the existing understanding of long COVID and associated phenomena, and facilitate discussion among scientific researchers and medical experts. The proposed research framework allows studies conducted under different conditions to be compared and integrated. The framework can be applied to specific syndromic aspects of interest, guide the design of observational studies and randomised controlled trials, and address relevant prognostic and diagnostic problems in this domain. This approach offers critical opportunities to better understand who is at greatest risk of developing long COVID, potential pathways to quicker recovery, and who to target for future interventions.

METHODS

This manuscript complies with the Reporting Standards for Bayesian Network Modelling ¹¹. A complete checklist, as well as the key roles of the authors and collaborators involved, are summarised in the Supplementary Information (Supplementary Tables 2 and 3).

Preliminary DAG development

A preliminary causal DAG (Supplementary Information [Supplementary Fig. 1]) was drafted based on published literature (GPC, YW, and SM) and designed as an extension to our earlier expert respiratory BN¹². This was later revised to separate and extract an initial general framework model (Supplementary Information [Supplementary Fig. 2]), and became the long COVID respiratory model (described at the end of the Results section). The framework model was designed around the development and evolution of organ dysfunctions manifesting as long COVID, with the respiratory system still used as a primary reference during development.

A dynamic structure with explicit time points was further chosen to demarcate different phases of the disease. Subsequently, this structure was presented to clinical domain experts in infectious diseases (TS) and long COVID (GM; see Acknowledgment section) via a knowledge elicitation session (SM, GP, and YW) using a knowledge engineering approach to consolidate understanding of the problem domain and structure development¹³.

Developing a general framework

After the session, the preliminary causal DAG was refined to improve its generality. A key design choice was to allow the framework to support alternative definitions of long COVID and to be applicable to different organs and systems. Consequently, the framework was revised to detach time periods from specific durations and to leave the selection of organs or systems to the needs of a specific research study.

The first session also identified the need to clarify the causal semantics of the DAG, which could be achieved with qualitative parametrisation ¹⁴. The general framework was qualitatively parametrised by a biomathematician with domain knowledge (YW) and further reviewed by the two remaining modellers (SM and GPC) to assess its ability to represent the expected patterns of disease progression —that is, with the sole concern of capturing the intended qualitative behaviour, including the direction and approximate size of probability changes in response to new evidence. These features are independent of any study or dataset. The DAG structure alone does not capture them; by contrast, qualitative parametrisation does. This approach ensured our framework could represent the broad classes of long COVID clinical presentations we intended. Additionally, it helped us articulate modelling concepts during subsequent validation sessions and demonstrated the model’s capability to improve understanding of the underlying structure using hypothetical medical scenarios.

Validation of the general framework

The general framework was presented to an immunobiologist with expertise in long COVID (CP) for validation of the causal structures. Illustrative scenarios were presented to a clinical domain expert (TS) to demonstrate the qualitative behaviour of the parametrised model. Each scenario depicted a situation in which one or more observations have been made of an individual, and the model provides both inferences about the individual’s current underlying disease state as well as predictions of their future disease state and symptoms. In addition, minor revisions to parameters and node labels were made to better reflect their intended states (e.g., ‘mild infection’ was reworded as ‘mild disease’, and ‘irreversible organ dysfunction’ was changed to ‘persistent organ dysfunction’). The relevance of the periods, concepts, and language selected for the framework, particularly concerning ADAPT, the largest observational longitudinal study of Australian adults with PCR-confirmed mild-to-moderate COVID-19, was subsequently validated (TS)¹⁵.

Graphical structures and causal language were reviewed by consumer advisors (BD and BS, see Acknowledgment section) and domain experts (TS), and revised further based on their feedback. We tested the revised framework by using it to develop a secondary causal DAG for the respiratory and immune systems. This pulmonary model was further developed and is described later. Additionally, illustrative simulations are included in the Supplementary Information. These simulations offer a conceptual framework for future validation studies.

Statistics and reproducibility

We describe the model structure and demonstrate its application in four scenarios. The models and conditional probability tables were created using the GeNIe academic application version 4.0, which primarily employs a graphical user interface¹⁶. Each node is labelled with a capital letter, a number, and a brief description. Nodes are represented with conditional probability tables that are standard for discrete BNs, however these can be replaced in an analysis with any suitable continuous or discrete conditional probability representation. Comprehensive variable dictionaries, including references for each node and arc, are provided in the Supplementary Information (Supplementary Tables 4 and 5).

Ethics approval

Ethics approval was granted by the Monash University Human Research Ethics Committee (Project ID 26942).

RESULTS

A general framework on post-COVID-19 phenomena

The general framework (Fig. 2) models the natural history of SARS-CoV-2 infection across a prolonged period of time (t) from t₁ (the start of acute infection) to t₄ (e.g., 2 years post-infection). We broadly divide COVID-19 into mild (e.g., ambulatory, M1) and severe (e.g., hospitalised, V1) cases during the acute phase of infection, where a mild case can progress to become severe. Both mild (M1) and severe (S1) COVID-19 can cause reversible organ dysfunction (R1) or persistent organ damage and dysfunction (P1). In the first instance, reversible organ injury is followed by recovery. When organ injury is severe, homeostatic self-repair may fail and the injury will persist into future time periods. Any reversible (R1) or persistent (P1) organ dysfunction may manifest as patient-reported symptoms (S1). In this context, different pathobiological mechanisms causing organ dysfunction can give rise to similar symptoms.

Fig. 2. Qualitative dynamic causal Bayesian network that represents the natural history of long COVID (which is referred to in the text as the general framework).

Four different time periods of interest were chosen, defined by the start of acute infection (t₁), which can be confirmed by, e.g., PCR, suspected on the basis of less direct evidence, or otherwise remain latent; the end of the acute infection (t₂); beyond acute infection (t₃, e.g., 3 months post t₁), and long-term sequelae (t₄, e.g., 1-to-2 years post t₁). This dynamic model encompasses six variables at t₁, identified with a capital letter (M1, mild disease; V1, severe disease; T1, treatment; R1, reversible organ dysfunction; P1, persistent organ dysfunction; S1, symptoms); three of them (R, I, and S) can further change their status throughout the follow-up period (t₂ to t₄). An emerging mechanistic pathway (E) can arise at any time point. In this general framework, E is the child of R2 and P2, and can directly influence the development of unresolved and sustained dysfunctions at t₃. Emerging mechanisms may also lead to emerging symptoms (ES3). For simplicity, no background factors are included in the models. In diagnostic problems, inference flows opposite to the direction of the network arrows from (observed) effects to their causes. Reported symptoms or clusters of symptoms (S1 or S2) during the acute phase of COVID-19 (i.e., between t₁ and t₂) propagate backwards to influence the estimated probability of reversible or persistent organ damage and dysfunction (R1, R2, P1, and P2). For prognostication, by contrast, information propagates forward along causal links, following the direction of the network arrows. For example, mild COVID-19 (M1) has a direct causal effect on the probability of reversible organ dysfunction (R1 and R2 via t₁) and the probability of receiving antiviral treatment (T1). This could affect the probability of subsequent symptoms (S1) which can occur across the depicted follow-up period (S2, S3, and S4), conditional on the presence of reversible (R2, R3, and R4) and/or persistent organ dysfunction (P2, P3, and P4). The model variable dictionary is available in the Supplementary Information (Supplementary Table 4).

It is important to note that the severity of specific organ damage and dysfunction may fluctuate over time. As a result, the presence of symptoms caused by the same underlying mechanism can also fluctuate (e.g., recurrent pattern, S3), which may pose challenges for data collection. Guided by any clinical indicators of the disease status (mild [M1] or severe [V1] COVID-19), the acute infection may (or may not) be treated (t₁), leading to an updated functional status for relevant organs at the end of acute infection (t₂). Under the circumstance where organ dysfunction continues beyond the acute phase (passing from t₂ into t₃ and t₄), symptoms could persist or recur (S3 and S4). As the (dys)functions of different organs interact as a dynamic system, new pathologic mechanistic pathways (E) may emerge and give rise to organ dysfunctions that were not present previously, which may subsequently give rise to new symptoms (ES3). New symptoms may also appear due to a worsening of pre-existing organ dysfunction (R3 or P3).

Illustrative scenarios

Guided by qualitative parametrisation, we present four scenarios (Fig. 3) to illustrate and test the face validity of the general framework for post-COVID-19 phenomena. In the following subsections, probabilities have all been expressed as percentages rounded to the nearest whole number. The states of the input variables for each scenario are characterised as yes or reported and are therefore considered to be ‘observed evidence’ which may be an imperfect measure of the concept in question (for example, someone may fail to report the presence of cough, or it may be incorrectly reported as present when it is not). The four scenarios are intended to be broadly illustrative for any strain of SARS-CoV-2 or pandemic era, but otherwise assume natural infection in the absence of immunity from vaccination or prior infection. The selected parameters are described in detail in the Supplementary Information (Supplementary Table 4), based on evidence from the literature.

Fig. 3. Four clinical scenarios (labelled A, B, C, or D on each node).

Probabilities have all been expressed as percentages rounded to the nearest whole number. When a node has evidence entered for it in a given scenario, the evidence is shown with a black background; otherwise, the probability for that node is shown along with a bar coloured differently for each scenario (green, red, purple and blue, respectively). In scenario A, there is one piece of evidence, that M1: Mild disease = yes. In scenario B, the evidence instead is that V1: Severe disease = yes. In scenario C, the only evidence is that V1: Symptoms are reported at t₁. In scenario D, there are two pieces of evidence, that symptoms are reported at t₁ (S1: Symptoms) and t₃ (S3: Symptoms). Across the four scenarios, the probability of P1: Persistent organ dysfunction being true, for example, is 1% (scenario A), 7% (scenario B), 3% (scenario C) and 36% (scenario D).

Scenario A (green): Mild disease observed at t₁

Consider an adult with observed mild COVID-19 (M1) at t₁. The model depicts a 10% probability of progressing to severe disease (V1) which gives rise to a high probability of developing reversible organ dysfunction (R1, 73%), and a very small probability (1%) of persistent organ dysfunction (P1) at t₁. The mechanisms are not directly observable; what may be observed is the reporting of symptoms (S1, e.g., cough or fatigue) which occurs with a moderately high probability (61%). The probability of sustained reversible organ dysfunction steadily drops from t₁ to a very low level at t₄ (R4, 3%) as the underlying tissue damage and dysfunction recovers. Under this scenario, persistent organ dysfunction (P1) is rare, but its probability seldom decreases — here rising from 1% t₁ to 2% at t₄. The probability of reported symptoms would also decrease from the initial 61% (driven by reversible dysfunction R1) to 4% over the modelled period (S4 at t₄), with an increasing relative attribution of symptoms to persistent organ damage and dysfunction (P4).

Scenario B (red): Severe disease observed at t₁

The cohort with severe acute COVID-19 (V1) at t₁ certainly experiences reversible organ dysfunction (R1, probability 100%). Likewise, they experience a higher probability of persistent organ dysfunction (P1, 7%) compared with those with mild disease in scenario A (P1, 1%). In this context, the probability of reporting symptoms is almost certain (S1, 94%). The severity of the disease drives the probability of treatment (T1), which may precede functional recovery, decreasing reversible organ dysfunction from certainty at t₁ (R1) to a modest probability at t₂ (R2, 13%). As expected, the probability of reported symptoms also declines from near certainty at t₁ (S1, 94%) to a small probability at t₄ (S4, 9%), predominantly driven by persistent organ dysfunction (P4) in the long term.

Scenario C (purple): Symptoms reported at t₁, indicating acute COVID-19 disease

In the absence of other information about their disease status, reported symptoms (S1) at t₁ leads to a high chance of mild acute COVID-19 disease (M1, 79%) with a modest probability of progressing to severe disease (V1, 12%). In contrast with scenario A, the cohort that reports symptoms is slightly enriched with those patients with severe disease (V1, 12% versus 10%) and persistent organ dysfunction (P1, 3% versus 1%) at t₁.

Scenario D (blue): Symptoms reported at t₁ and t₃, indicating long COVID

Comparing with scenario C, the probability of severe disease and persistent organ dysfunction is further exaggerated in this cohort who report symptoms at both t₁ and t₃ (S1 and S3). This scenario reflects many operational definitions of long COVID, including the one used in the ADAPT study, which describes ongoing physical symptoms (e.g., dyspnea, chest pain, fatigue/malaise) and/or neuropsychiatric symptoms lasting longer than three months after acute SARS-CoV-2 infection ¹⁵. Recurrent and persisting symptoms (S3) at t₃ are highly indicative of persistent organ dysfunction (P3, 40%), which may further give rise to newly emerging symptoms (ES3, 9%), and a moderate probability of further ongoing and recurrent symptoms beyond t₃ (S4, 45%).

Applying the general framework to the respiratory system

The general framework can be used to organise identified or hypothesised mechanisms for acute and post-acute COVID-19-related pulmonary dysfunction.

In Fig. 4 we select some potential mechanisms of respiratory post-acute sequelae of COVID-19, such as (1) impaired gas exchange in patients with no history of intubation and (2) pulmonary fibrosis^17,18. These mechanisms are mapped to the general framework and, alongside additional plausible pathways mediated by volutrauma, lead to the development of cough, dyspnea, and fatigue.

Fig. 4. Application of the general framework to the respiratory system, including initial SARS-CoV-2 infection, pulmonary symptoms, and the emergence of fatigue.

Hypotheses and mechanisms (e.g., mechanical ventilation and volutrauma) have been organised by attaching them to their corresponding general framework node classes (e.g., T1 and P2-P4), which are now represented by boxes. The general framework is visible in the background, and the time points in this example remain aligned with those in Fig. 2. URT inflam. upper respiratory tract inflammation, SaO₂ oxygen saturation of arterial blood, alveolar inflam. alveolar inflammation, mech. ventil. mechanical ventilation, impaired gas exch. impaired gas exchange, BBB dysfunc. blood brain barrier dysfunction. The model variable dictionary is included in the Supplementary Information (Supplementary Table 5).

To organise the existing respiratory hypotheses, proposed or known mechanisms (such as alveolar inflammation for R1) and signs/symptoms (such as cough and dyspnea for S1) replace their general framework node classes (for these examples, R1 and S1, respectively). These nodes are presented below with a narrative description, and a node mapping is provided in full in the Supplementary Information (Supplementary Table 5).

Alveolar inflammation is a proposed latent mechanism at t₁ that can give rise to cough and dyspnea/respiratory distress^12,19. Of the many potential treatment options during t₁, we have included antivirals (e.g., nirmatrelvir/ritonavir) and mechanical ventilation as examples. It has been suggested that antivirals may reduce pulmonary viral replication, potentially ameliorating more serious consequences caused by SARS-CoV-2 induced inflammation and tissue damage²⁰. Mechanical ventilation may be used to ensure the patient has adequate pulmonary function, but it can also lead to volutrauma (a type of ventilator-induced lung injury due to lung overdistension), with the further release of pro-inflammatory cytokines that may induce or aggravate ongoing lung injury (arrow A), especially among those with pre-existing comorbidities like chronic obstructive pulmonary disease²¹.

When homeostatic mechanisms fail, transudative fluid can accumulate in the lower airways (alveoli) at t₂ which can culminate in acute respiratory distress syndrome (ARDS). ARDS contributes to worsening of dyspnea/respiratory distress and can result in chronic pulmonary inflammation, macrophage dysregulation, and lung remodelling. In some instances, it has been suggested that lung remodelling may progress to long term pulmonary fibrosis (arrow B) owing to diffuse alveolar damage and the formation of alveolar hyaline membranes^22,23, leading to chronic hypoxia and fatigue. Additional proposed pathological mechanisms involved in the development of ARDS include disseminated pulmonary micro-immunothromboses (t₂, possibly t₃) leading to alveolar-capillary dysfunction, impaired gas exchange, and thereby dyspnea/respiratory distress and fatigue²⁴. The extent to which these factors contribute to long-term respiratory outcomes may be influenced by additional circumstances, such as volutrauma at t₂, t₃, and t₄ and emerging mechanisms.

It has been hypothesised that emerging mechanistic pathways for long COVID could arise from the persistence of viral antigens (e.g., spike protein) or SARS-CoV-2 remnants in the lung parenchyma leading to prolonged immune activation, chronic pulmonary inflammation, and persistent tissue damage and dysfunction²⁵. Analogous mechanisms (such as immune activation and tissue damage) have also been suggested to emerge from the persistence of SARS-CoV-2 in the extrapulmonary tissues². One hypothesis holds that reservoirs of SARS-CoV-2 can increase circulating spike protein and further enhance endothelial and blood-brain barrier (BBB) dysfunction, leading to the emergence or worsening of preexisting COVID-driven fatigue at t₃ and/or t₄²⁶. We note that pulmonary fibrosis and volutrauma may compound these issues.

In the causal model, we have represented the various proposed neuropathological mechanisms for fatigue as reversible, running alongside R2, R3, and R4. However, some mechanisms may be persistent, and we have depicted hypotheses of this kind with a dashed outline. The general framework allows for both hypothetical forms to be represented and jointly tested, by (for example) showing the emergence, maintenance and/or resolution of associated symptoms over the expected time frames.

DISCUSSION

We have introduced a causal modelling framework, consisting of causal DAGs and BNs, to represent some of the pathobiological mechanisms underpinning long COVID proposed by the scientific community. The face validity of the proposed causal structures has been assessed through qualitative parametrisation (Fig. 3) and statistical simulations, supporting its use for improving communications among researchers and comparisons of research studies. However, it has yet to be validated using data from randomised controlled trials or non-randomised studies of interventions, which would be needed prior to its use within decision support systems.

In examining the structure of an existing COVID causal and progression model, the proposed general framework retained the organ-system-based architecture, introduced a distinction between reversible and persistent organ dysfunction, demarcated four key periods from the initial acute infection to the development of long-term sequelae, and introduced emerging mechanistic pathways that may explain the development of new symptoms after acute infection¹².

We have also shown how a general modelling framework can depict the current understanding of long COVID’s complex respiratory pathology. To ensure clarity and reproducibility, specific long COVID case definitions (Supplementary Information, Supplementary Table 1) are preferred. However, within the general modelling framework, intentionally broad terms (e.g., mild versus severe; t₁ versus t₂; any post-COVID-19 morbidity over a 2-year period) were selected. This higher level of abstraction in causal modelling is necessary to map previous research findings across different studies and to make the approach generalisable to other infection-associated chronic conditions. When applying the framework to a specific research question, it is important to tailor its variables to the question being investigated, as we did when organising hypotheses for the respiratory system in Fig. 4. Although omitted here for simplicity, it is also critical to depict the influence of relevant patient characteristics, such as age, sex, and comorbidities. While this omission might be considered a limitation, we believe that confounder adjustment is best addressed within the context of individual studies; for instance, the statistical simulations provided in the Supplement illustrate a scenario where confounders can be implicitly accounted for, eliminating the need for explicit inclusion in the model.

In general, we see three major applications of the proposed causal BNs. First, to articulate a causal understanding of long COVID, the general framework can be applied to each syndromic aspect of interest (e.g., the respiratory system, Fig. 4). Second, based on the framework and a common language, clinical and basic science studies can be designed to answer more explicit causal questions, and where relevant, incorporate additional factors such as COVID-19 vaccination, new types of SARS-CoV-2 strains, and newly identified disease mechanisms. In this context, Rubin’s potential outcome framework and Pearl’s do-calculus can be applied to assess the effects of treatment on clinical and mechanistic outcomes. To provide such assessments, the requirements need to be adhered to — i.e., the known relevant background factors and confounders must also be included based on causal inference principles²⁷. Using the general framework to help answer these kinds of causal questions would involve the following steps:

1. Formulate the scientific question.

2. Use the general framework to develop a knowledge DAG that addresses the scientific question.

3. Use the knowledge DAG to collect or identify suitable existing data.

4. Use the knowledge DAG to create an analysis DAG that aligns with transformed data.

5. Use the analysis DAG to design statistical analyses for causal inference.

6. Run the analysis, evaluate and iterate.

A hypothetical example of this process for investigating causal hypotheses is provided in the Supplementary Information.

Third, since the framework is underpinned by a qualitative dynamic causal BN (Fig. 2), it can support both diagnostic and prognostic applications in long COVID. This depends on further clarification of disease mechanisms, which the framework aims to facilitate. A clearer understanding of these mechanisms allows the general BN structure to be tailored to specific pathophysiological processes, parametrised with real-world data, and used as a predictive tool. Moreover, the framework guides how and when data should be collected to inform diagnosis or prognosis, and can assist prognostic studies by clarifying what needs to be accounted for given the dynamic nature of long COVID phenomena.

Uncertainties around the problem domain (e.g., what long COVID is, the set of associated conditions that it represents, and their underlying mechanisms) have in turn led to difficulties in developing and agreeing on a unified causal language. By making use of a knowledge engineering process in which we examined and validated the framework with domain experts, we were able to more clearly understand these shortcomings and explicitly account for them. As a consequence, we feel confident that the framework can be applied to the variety of syndromes that fall within the long COVID spectrum and might eventually be extended to other debilitating long-term phenomena such as myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS), since shared symptoms suggest the possibility of common pathomechanisms¹⁰.

Traditional studies or data-only methodologies that lack an explicit representation of the proposed causal structure, including many statistical or classification machine learning techniques, fail to capture the time-varying nature of symptoms emerging or persisting beyond the acute phase of SARS-CoV-2 infection²⁸. This is because the key events in the natural history of a long COVID case are latent. Here we demonstrate how a research framework based on causal DAGs and BNs helps to overcome these shortcomings by providing a graphical structure that enables the selection of plausible clinical surrogates to capture the causal effect of interest. In the future, quantitative parametrisation of these networks based on data arising from randomised controlled trials or non-randomised studies of interventions could yield meaningful new insights. Ultimately, a BN parametrised with actual patient data could inspire the discovery of latent relationships between symptoms and hypothesised disease mechanisms, and improve the prospects for predicting outcomes among those affected by long COVID. A quantitatively parametrised network can aid in determining the probability of long-term outcomes being attributed to COVID-19. It can also clarify the pathobiological overlaps between long COVID and other post-acute infection syndromes.

Our framework is readily available for external validation, which may include alternative long COVID definitions and hypotheses, time frames, organs and systems, and contrasting perspectives between people with lived experience and clinicians. While we have not yet tested it directly with existing data sources, we believe this offers a way forward for prioritising causal inference in long COVID research.

Author contributions

Conceptualisation: S.M., Y.W., T.S.; Formal analysis: G.P.C., S.M., Y.W.; Validation: T.S. and C.P.; Writing – Original draft preparation: G.P.C.; Writing – Review & editing: G.P.C., S.M., M.J.E., C.P., A.N., T.S., and Y.W.; Funding acquisition: AN and TS.

Peer review

Peer review information

Communications Medicine thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

All data supporting the findings of this study are available within the article, its Supplementary Information, and through the Open Science Framework (OSF; Files tab). The source data for Fig. 3 are provided in the Supplementary Information (Supplementary Table 4) under the column “Qualitative parameterisation (illustrative model assumptions)” and are also accessible via the OSF (Files tab, Supplement folder, Supplementary tables [Supplementary Table 4]). Source data for the statistical simulations (Supplementary Data and Supplementary Data 2) are provided in the OSF (Files tab, Supplement folder).

Code availability

Simulations were conducted in R version 4.4.1 ²⁹. The code used for statistical simulations is available in the Open Science Framework (Files Tab, Supplement folder).

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s43856-026-01488-8.